LMFDB - Embedded newform 324.3.f.r.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(55,324)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("324.55");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.f (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.119023932416481.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 3 x^{10} + 11 x^{9} - 5 x^{8} - 14 x^{7} + 29 x^{6} - 28 x^{5} - 20 x^{4} + \cdots + 64 $ x^12 - 2x^11 - 3x^10 + 11x^9 - 5x^8 - 14x^7 + 29x^6 - 28x^5 - 20x^4 + 88x^3 - 48x^2 - 64*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			55.1
Root			$-1.36237 - 0.379393i$ of defining polynomial
Character	$\chi$	$=$	324.55
Dual form			324.3.f.r.271.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.91597 + 0.573621i) q^{2} +(3.34192 - 2.19809i) q^{4} +(-2.18740 - 3.78869i) q^{5} +(1.84918 + 1.06762i) q^{7} +(-5.14216 + 6.12848i) q^{8} +O(q^{10})$	\(q+(-1.91597 + 0.573621i) q^{2} +(3.34192 - 2.19809i) q^{4} +(-2.18740 - 3.78869i) q^{5} +(1.84918 + 1.06762i) q^{7} +(-5.14216 + 6.12848i) q^{8} +(6.36427 + 6.00429i) q^{10} +(-10.9277 - 6.30914i) q^{11} +(-4.63163 - 8.02222i) q^{13} +(-4.15539 - 0.984811i) q^{14} +(6.33682 - 14.6917i) q^{16} +14.6381 q^{17} +34.5778i q^{19} +(-15.6380 - 7.85338i) q^{20} +(24.5563 + 5.81976i) q^{22} +(-35.3255 + 20.3952i) q^{23} +(2.93057 - 5.07589i) q^{25} +(13.4758 + 12.7136i) q^{26} +(8.52653 - 0.496747i) q^{28} +(-9.52010 + 16.4893i) q^{29} +(-0.860391 + 0.496747i) q^{31} +(-3.71373 + 31.7838i) q^{32} +(-28.0462 + 8.39671i) q^{34} -9.34128i q^{35} -66.4263 q^{37} +(-19.8346 - 66.2502i) q^{38} +(34.4668 + 6.07660i) q^{40} +(-12.9434 - 22.4187i) q^{41} +(-36.4816 - 21.0627i) q^{43} +(-50.3877 + 2.93554i) q^{44} +(55.9836 - 59.3401i) q^{46} +(30.1126 + 17.3855i) q^{47} +(-22.2204 - 38.4868i) q^{49} +(-2.70325 + 11.4063i) q^{50} +(-33.1121 - 16.6289i) q^{52} -12.2231 q^{53} +55.2024i q^{55} +(-16.0517 + 5.84275i) q^{56} +(8.78165 - 37.0540i) q^{58} +(-49.1301 + 28.3653i) q^{59} +(-36.8804 + 63.8788i) q^{61} +(1.36354 - 1.44529i) q^{62} +(-11.1164 - 63.0272i) q^{64} +(-20.2625 + 35.0956i) q^{65} +(-82.4391 + 47.5962i) q^{67} +(48.9192 - 32.1758i) q^{68} +(5.35836 + 17.8976i) q^{70} -75.5614i q^{71} -56.7185 q^{73} +(127.271 - 38.1035i) q^{74} +(76.0051 + 115.556i) q^{76} +(-13.4716 - 23.3334i) q^{77} +(64.5777 + 37.2839i) q^{79} +(-69.5232 + 8.12830i) q^{80} +(37.6591 + 35.5290i) q^{82} +(56.7179 + 32.7461i) q^{83} +(-32.0193 - 55.4590i) q^{85} +(81.9798 + 19.4289i) q^{86} +(94.8576 - 34.5279i) q^{88} +150.050 q^{89} -19.7794i q^{91} +(-73.2244 + 145.808i) q^{92} +(-67.6677 - 16.0370i) q^{94} +(131.005 - 75.6355i) q^{95} +(56.4426 - 97.7615i) q^{97} +(64.6505 + 60.9936i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} + 3 q^{4} + 2 q^{5} - 14 q^{8}+O(q^{10}) $ 12 * q + q^2 + 3 * q^4 + 2 * q^5 - 14 * q^8	$ 12 q + q^{2} + 3 q^{4} + 2 q^{5} - 14 q^{8} + 18 q^{10} - 6 q^{13} + 15 q^{16} + 20 q^{17} - 67 q^{20} - 48 q^{22} + 146 q^{26} - 96 q^{28} - 22 q^{29} + 31 q^{32} - 81 q^{34} + 108 q^{37} + 168 q^{38} + 81 q^{40} + 92 q^{41} - 336 q^{44} + 240 q^{46} + 66 q^{49} - 48 q^{50} + 117 q^{52} - 232 q^{53} - 312 q^{56} - 201 q^{58} - 54 q^{61} + 624 q^{62} - 510 q^{64} + 82 q^{65} + 53 q^{68} - 264 q^{70} - 156 q^{73} + 383 q^{74} + 192 q^{76} - 168 q^{77} - 754 q^{80} + 300 q^{82} - 66 q^{85} - 144 q^{86} + 336 q^{88} + 500 q^{89} - 504 q^{92} - 216 q^{94} + 204 q^{97} + 814 q^{98}+O(q^{100}) $ 12 * q + q^2 + 3 * q^4 + 2 * q^5 - 14 * q^8 + 18 * q^10 - 6 * q^13 + 15 * q^16 + 20 * q^17 - 67 * q^20 - 48 * q^22 + 146 * q^26 - 96 * q^28 - 22 * q^29 + 31 * q^32 - 81 * q^34 + 108 * q^37 + 168 * q^38 + 81 * q^40 + 92 * q^41 - 336 * q^44 + 240 * q^46 + 66 * q^49 - 48 * q^50 + 117 * q^52 - 232 * q^53 - 312 * q^56 - 201 * q^58 - 54 * q^61 + 624 * q^62 - 510 * q^64 + 82 * q^65 + 53 * q^68 - 264 * q^70 - 156 * q^73 + 383 * q^74 + 192 * q^76 - 168 * q^77 - 754 * q^80 + 300 * q^82 - 66 * q^85 - 144 * q^86 + 336 * q^88 + 500 * q^89 - 504 * q^92 - 216 * q^94 + 204 * q^97 + 814 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.91597	+	0.573621i	−0.957987	+	0.286811i
$2$	−1.91597	+	0.573621i	−0.957987	+	0.286811i
$3$		0			0
$3$		0			0
$4$	3.34192	−	2.19809i	0.835479	−	0.549522i
$5$	−2.18740	−	3.78869i	−0.437480	−	0.757737i	0.560014	−	0.828483i	$-0.310796\pi$
$5$	−2.18740	−	3.78869i	−0.437480	−	0.757737i	−0.997494	+	0.0707454i	$0.977462\pi$
$6$		0			0
$7$	1.84918	+	1.06762i	0.264168	+	0.152518i	0.626235	−	0.779635i	$-0.284595\pi$
$7$	1.84918	+	1.06762i	0.264168	+	0.152518i	−0.362066	+	0.932152i	$0.617929\pi$
$8$	−5.14216	+	6.12848i	−0.642770	+	0.766059i
$9$		0			0
$10$	6.36427	+	6.00429i	0.636427	+	0.600429i
$11$	−10.9277	−	6.30914i	−0.993432	−	0.573558i	−0.0871333	−	0.996197i	$-0.527771\pi$
$11$	−10.9277	−	6.30914i	−0.993432	−	0.573558i	−0.906298	+	0.422639i	$0.861104\pi$
$12$		0			0
$13$	−4.63163	−	8.02222i	−0.356279	−	0.617094i	0.631057	−	0.775737i	$-0.282622\pi$
$13$	−4.63163	−	8.02222i	−0.356279	−	0.617094i	−0.987336	+	0.158643i	$0.949288\pi$
$14$	−4.15539	−	0.984811i	−0.296814	−	0.0703437i
$15$		0			0
$16$	6.33682	−	14.6917i	0.396051	−	0.918228i
$17$	14.6381			0.861063			0.430531	−	0.902576i	$-0.358326\pi$
$17$	14.6381			0.861063			0.430531	+	0.902576i	$0.358326\pi$
$18$		0			0
$19$			34.5778i			1.81989i	0.414734	+	0.909943i	$0.363875\pi$
$19$			34.5778i			1.81989i	−0.414734	+	0.909943i	$0.636125\pi$
$20$	−15.6380	−	7.85338i	−0.781899	−	0.392669i
$21$		0			0
$22$	24.5563	+	5.81976i	1.11620	+	0.264534i
$23$	−35.3255	+	20.3952i	−1.53589	+	0.886747i	−0.536818	+	0.843698i	$0.680374\pi$
$23$	−35.3255	+	20.3952i	−1.53589	+	0.886747i	−0.999073	+	0.0430488i	$0.986293\pi$
$24$		0			0
$25$	2.93057	−	5.07589i	0.117223	−	0.203036i
$26$	13.4758	+	12.7136i	0.518300	+	0.488983i
$27$		0			0
$28$	8.52653	−	0.496747i	0.304519	−	0.0177410i
$29$	−9.52010	+	16.4893i	−0.328279	+	0.568596i	−0.982171	−	0.187992i	$-0.939802\pi$
$29$	−9.52010	+	16.4893i	−0.328279	+	0.568596i	0.653891	+	0.756589i	$0.273135\pi$
$30$		0			0
$31$	−0.860391	+	0.496747i	−0.0277546	+	0.0160241i	−0.513813	−	0.857902i	$-0.671768\pi$
$31$	−0.860391	+	0.496747i	−0.0277546	+	0.0160241i	0.486059	+	0.873926i	$0.338434\pi$
$32$	−3.71373	+	31.7838i	−0.116054	+	0.993243i
$33$		0			0
$34$	−28.0462	+	8.39671i	−0.824887	+	0.246962i
$35$		−	9.34128i		−	0.266894i
$36$		0			0
$37$	−66.4263			−1.79530			−0.897652	−	0.440705i	$-0.854729\pi$
$37$	−66.4263			−1.79530			−0.897652	+	0.440705i	$0.854729\pi$
$38$	−19.8346	−	66.2502i	−0.521963	−	1.74343i
$39$		0			0
$40$	34.4668	+	6.07660i	0.861671	+	0.151915i
$41$	−12.9434	−	22.4187i	−0.315693	−	0.546797i	0.663891	−	0.747829i	$-0.268904\pi$
$41$	−12.9434	−	22.4187i	−0.315693	−	0.546797i	−0.979585	+	0.201032i	$0.935570\pi$
$42$		0			0
$43$	−36.4816	−	21.0627i	−0.848409	−	0.489829i	0.0117046	−	0.999931i	$-0.496274\pi$
$43$	−36.4816	−	21.0627i	−0.848409	−	0.489829i	−0.860114	+	0.510102i	$0.829608\pi$
$44$	−50.3877	+	2.93554i	−1.14517	+	0.0667167i
$45$		0			0
$46$	55.9836	−	59.3401i	1.21704	−	1.29000i
$47$	30.1126	+	17.3855i	0.640694	+	0.369905i	0.784882	−	0.619646i	$-0.212724\pi$
$47$	30.1126	+	17.3855i	0.640694	+	0.369905i	−0.144188	+	0.989550i	$0.546057\pi$
$48$		0			0
$49$	−22.2204	−	38.4868i	−0.453477	−	0.785445i
$50$	−2.70325	+	11.4063i	−0.0540650	+	0.228126i
$51$		0			0
$52$	−33.1121	−	16.6289i	−0.636771	−	0.319786i
$53$	−12.2231			−0.230624			−0.115312	−	0.993329i	$-0.536787\pi$
$53$	−12.2231			−0.230624			−0.115312	+	0.993329i	$0.536787\pi$
$54$		0			0
$55$			55.2024i			1.00368i
$56$	−16.0517	+	5.84275i	−0.286637	+	0.104335i
$57$		0			0
$58$	8.78165	−	37.0540i	0.151408	−	0.638862i
$59$	−49.1301	+	28.3653i	−0.832714	+	0.480768i	−0.854781	−	0.518989i	$-0.826309\pi$
$59$	−49.1301	+	28.3653i	−0.832714	+	0.480768i	0.0220670	+	0.999756i	$0.492975\pi$
$60$		0			0
$61$	−36.8804	+	63.8788i	−0.604597	+	1.04719i	0.387518	+	0.921862i	$0.373333\pi$
$61$	−36.8804	+	63.8788i	−0.604597	+	1.04719i	−0.992115	+	0.125331i	$0.960001\pi$
$62$	1.36354	−	1.44529i	0.0219926	−	0.0233112i
$63$		0			0
$64$	−11.1164	−	63.0272i	−0.173694	−	0.984800i
$65$	−20.2625	+	35.0956i	−0.311730	+	0.539932i
$66$		0			0
$67$	−82.4391	+	47.5962i	−1.23043	+	0.710392i	−0.967121	−	0.254318i	$-0.918149\pi$
$67$	−82.4391	+	47.5962i	−1.23043	+	0.710392i	−0.263314	+	0.964710i	$0.584816\pi$
$68$	48.9192	−	32.1758i	0.719400	−	0.473173i
$69$		0			0
$70$	5.35836	+	17.8976i	0.0765479	+	0.255681i
$71$		−	75.5614i		−	1.06424i	−0.846667	−	0.532122i	$-0.821395\pi$
$71$		−	75.5614i		−	1.06424i	0.846667	−	0.532122i	$-0.178605\pi$
$72$		0			0
$73$	−56.7185			−0.776965			−0.388483	−	0.921456i	$-0.627001\pi$
$73$	−56.7185			−0.776965			−0.388483	+	0.921456i	$0.627001\pi$
$74$	127.271	−	38.1035i	1.71988	−	0.514912i
$75$		0			0
$76$	76.0051	+	115.556i	1.00007	+	1.52048i
$77$	−13.4716	−	23.3334i	−0.174955	−	0.303032i
$78$		0			0
$79$	64.5777	+	37.2839i	0.817439	+	0.471949i	0.849533	−	0.527536i	$-0.176884\pi$
$79$	64.5777	+	37.2839i	0.817439	+	0.471949i	−0.0320934	+	0.999485i	$0.510217\pi$
$80$	−69.5232	+	8.12830i	−0.869040	+	0.101604i
$81$		0			0
$82$	37.6591	+	35.5290i	0.459257	+	0.433280i
$83$	56.7179	+	32.7461i	0.683349	+	0.394532i	0.801116	−	0.598510i	$-0.204240\pi$
$83$	56.7179	+	32.7461i	0.683349	+	0.394532i	−0.117767	+	0.993041i	$0.537574\pi$
$84$		0			0
$85$	−32.0193	−	55.4590i	−0.376698	−	0.652459i
$86$	81.9798	+	19.4289i	0.953254	+	0.225917i
$87$		0			0
$88$	94.8576	−	34.5279i	1.07793	−	0.392362i
$89$	150.050			1.68595			0.842977	−	0.537950i	$-0.180801\pi$
$89$	150.050			1.68595			0.842977	+	0.537950i	$0.180801\pi$
$90$		0			0
$91$		−	19.7794i		−	0.217356i
$92$	−73.2244	+	145.808i	−0.795918	+	1.58486i
$93$		0			0
$94$	−67.6677	−	16.0370i	−0.719869	−	0.170606i
$95$	131.005	−	75.6355i	1.37900	−	0.796163i
$96$		0			0
$97$	56.4426	−	97.7615i	0.581883	−	1.00785i	−0.413373	−	0.910562i	$-0.635650\pi$
$97$	56.4426	−	97.7615i	0.581883	−	1.00785i	0.995256	−	0.0972889i	$-0.0310171\pi$
$98$	64.6505	+	60.9936i	0.659699	+	0.622384i
$99$		0			0
$100$	−1.36354	−	23.4048i	−0.0136354	−	0.234048i
$101$	21.9708	−	38.0545i	0.217532	−	0.376777i	−0.736521	−	0.676415i	$-0.763533\pi$
$101$	21.9708	−	38.0545i	0.217532	−	0.376777i	0.954053	+	0.299638i	$0.0968659\pi$
$102$		0			0
$103$	−66.4269	+	38.3516i	−0.644921	+	0.372345i	−0.786508	−	0.617581i	$-0.788113\pi$
$103$	−66.4269	+	38.3516i	−0.644921	+	0.372345i	0.141587	+	0.989926i	$0.454780\pi$
$104$	72.9806	+	12.8667i	0.701736	+	0.123718i
$105$		0			0
$106$	23.4191	−	7.01141i	0.220935	−	0.0661454i
$107$			9.53448i			0.0891073i	0.999007	+	0.0445537i	$0.0141866\pi$
$107$			9.53448i			0.0891073i	−0.999007	+	0.0445537i	$0.985813\pi$
$108$		0			0
$109$	51.4021			0.471579			0.235790	−	0.971804i	$-0.424232\pi$
$109$	51.4021			0.471579			0.235790	+	0.971804i	$0.424232\pi$
$110$	−31.6653	−	105.766i	−0.287866	−	0.961513i
$111$		0			0
$112$	27.4031	−	20.4022i	0.244670	−	0.182162i
$113$	−0.914995	−	1.58482i	−0.00809730	−	0.0140249i	0.861948	−	0.506996i	$-0.169244\pi$
$113$	−0.914995	−	1.58482i	−0.00809730	−	0.0140249i	−0.870046	+	0.492971i	$0.835911\pi$
$114$		0			0
$115$	154.542	+	89.2248i	1.34384	+	0.775868i
$116$	4.42954	+	76.0319i	0.0381857	+	0.655447i
$117$		0			0
$118$	77.8611	−	82.5293i	0.659840	−	0.699401i
$119$	27.0684	+	15.6279i	0.227465	+	0.131327i
$120$		0			0
$121$	19.1104	+	33.1002i	0.157937	+	0.273556i
$122$	34.0197	−	143.546i	0.278850	−	1.17660i
$123$		0			0
$124$	−1.78346	+	3.55130i	−0.0143828	+	0.0286395i
$125$	−135.011			−1.08009
$126$		0			0
$127$		−	46.6614i		−	0.367413i	−0.982981	−	0.183706i	$-0.941190\pi$
$127$		−	46.6614i		−	0.367413i	0.982981	−	0.183706i	$-0.0588096\pi$
$128$	57.4525	+	114.382i	0.448848	+	0.893608i
$129$		0			0
$130$	18.6908	−	78.8653i	0.143775	−	0.606656i
$131$	100.596	−	58.0793i	0.767910	−	0.443353i	−0.0642183	−	0.997936i	$-0.520455\pi$
$131$	100.596	−	58.0793i	0.767910	−	0.443353i	0.832129	+	0.554583i	$0.187122\pi$
$132$		0			0
$133$	−36.9161	+	63.9406i	−0.277565	+	0.480756i
$134$	130.649	−	138.482i	0.974993	−	1.03345i
$135$		0			0
$136$	−75.2712	+	89.7090i	−0.553465	+	0.659625i
$137$	−53.9555	+	93.4536i	−0.393836	+	0.682143i	−0.992952	−	0.118519i	$-0.962185\pi$
$137$	−53.9555	+	93.4536i	−0.393836	+	0.682143i	0.599116	+	0.800662i	$0.295519\pi$
$138$		0			0
$139$	130.016	−	75.0646i	0.935365	−	0.540033i	0.0468609	−	0.998901i	$-0.485078\pi$
$139$	130.016	−	75.0646i	0.935365	−	0.540033i	0.888504	+	0.458868i	$0.151745\pi$
$140$	−20.5329	−	31.2178i	−0.146664	−	0.222984i
$141$		0			0
$142$	43.3436	+	144.774i	0.305237	+	1.01953i
$143$			116.886i			0.817388i
$144$		0			0
$145$	83.2970			0.574462
$146$	108.671	−	32.5349i	0.744323	−	0.222842i
$147$		0			0
$148$	−221.991	+	146.011i	−1.49994	+	0.986559i
$149$	−3.81611	−	6.60970i	−0.0256115	−	0.0443604i	0.852936	−	0.522016i	$-0.174820\pi$
$149$	−3.81611	−	6.60970i	−0.0256115	−	0.0443604i	−0.878547	+	0.477656i	$0.841487\pi$
$150$		0			0
$151$	−183.627	−	106.017i	−1.21607	−	0.702099i	−0.251996	−	0.967728i	$-0.581087\pi$
$151$	−183.627	−	106.017i	−1.21607	−	0.702099i	−0.964075	+	0.265629i	$0.914420\pi$
$152$	−211.909	−	177.805i	−1.39414	−	1.16977i
$153$		0			0
$154$	39.1957	+	36.9787i	0.254518	+	0.240121i
$155$	3.76404	+	2.17317i	0.0242841	+	0.0140204i
$156$		0			0
$157$	30.6558	+	53.0973i	0.195260	+	0.338199i	0.946986	−	0.321276i	$-0.104112\pi$
$157$	30.6558	+	53.0973i	0.195260	+	0.338199i	−0.751726	+	0.659476i	$0.770778\pi$
$158$	−145.116	−	34.3920i	−0.918456	−	0.217671i
$159$		0			0
$160$	128.542	−	55.4536i	0.803389	−	0.346585i
$161$	−87.0975			−0.540978
$162$		0			0
$163$		−	25.3264i		−	0.155377i	−0.996978	−	0.0776885i	$-0.975246\pi$
$163$		−	25.3264i		−	0.155377i	0.996978	−	0.0776885i	$-0.0247540\pi$
$164$	−92.5341	−	46.4706i	−0.564232	−	0.283357i
$165$		0			0
$166$	−127.454	−	30.2061i	−0.767795	−	0.181964i
$167$	−120.244	+	69.4230i	−0.720025	+	0.415707i	−0.814762	−	0.579796i	$-0.803132\pi$
$167$	−120.244	+	69.4230i	−0.720025	+	0.415707i	0.0947370	+	0.995502i	$0.469799\pi$
$168$		0			0
$169$	41.5960	−	72.0463i	0.246130	−	0.426310i
$170$	93.1606	+	87.8912i	0.548004	+	0.517007i
$171$		0			0
$172$	−168.216	+	9.80010i	−0.978000	+	0.0569773i
$173$	45.1000	−	78.1155i	0.260694	−	0.451534i	−0.705733	−	0.708478i	$-0.749382\pi$
$173$	45.1000	−	78.1155i	0.260694	−	0.451534i	0.966426	+	0.256944i	$0.0827155\pi$
$174$		0			0
$175$	10.8383	−	6.25748i	0.0619330	−	0.0357570i
$176$	−161.939	+	120.567i	−0.920107	+	0.685039i
$177$		0			0
$178$	−287.492	+	86.0718i	−1.61512	+	0.483549i
$179$		−	41.7114i		−	0.233025i	−0.993189	−	0.116512i	$-0.962829\pi$
$179$		−	41.7114i		−	0.233025i	0.993189	−	0.116512i	$-0.0371715\pi$
$180$		0			0
$181$	84.6616			0.467744			0.233872	−	0.972267i	$-0.424860\pi$
$181$	84.6616			0.467744			0.233872	+	0.972267i	$0.424860\pi$
$182$	11.3459	+	37.8967i	0.0623399	+	0.208224i
$183$		0			0
$184$	56.6579	−	321.367i	0.307923	−	1.74656i
$185$	145.301	+	251.668i	0.785409	+	1.36037i
$186$		0			0
$187$	−159.961	−	92.3536i	−0.855407	−	0.493869i
$188$	138.849	−	8.08919i	0.738557	−	0.0430276i
$189$		0			0
$190$	−207.615	+	220.063i	−1.09271	+	1.15823i
$191$	−152.525	−	88.0606i	−0.798562	−	0.461050i	0.0444058	−	0.999014i	$-0.485861\pi$
$191$	−152.525	−	88.0606i	−0.798562	−	0.461050i	−0.842968	+	0.537963i	$0.819194\pi$
$192$		0			0
$193$	166.424	+	288.255i	0.862300	+	1.49355i	0.869704	+	0.493574i	$0.164310\pi$
$193$	166.424	+	288.255i	0.862300	+	1.49355i	−0.00740395	+	0.999973i	$0.502357\pi$
$194$	−52.0645	+	219.685i	−0.268374	+	1.13240i
$195$		0			0
$196$	−158.856	−	79.7774i	−0.810490	−	0.407027i
$197$	−137.238			−0.696637			−0.348319	−	0.937376i	$-0.613247\pi$
$197$	−137.238			−0.696637			−0.348319	+	0.937376i	$0.613247\pi$
$198$		0			0
$199$		−	286.157i		−	1.43798i	−0.695023	−	0.718988i	$-0.744606\pi$
$199$		−	286.157i		−	1.43798i	0.695023	−	0.718988i	$-0.255394\pi$
$200$	16.0380	+	44.0609i	0.0801902	+	0.220305i
$201$		0			0
$202$	−20.2666	+	85.5143i	−0.100330	+	0.423338i
$203$	−35.2087	+	20.3278i	−0.173442	+	0.100137i
$204$		0			0
$205$	−56.6249	+	98.0772i	−0.276219	+	0.478425i
$206$	105.273	−	111.585i	0.511034	−	0.541672i
$207$		0			0
$208$	−147.210	+	17.2110i	−0.707738	+	0.0827451i
$209$	218.156	−	377.858i	1.04381	−	1.80793i
$210$		0			0
$211$	273.062	−	157.653i	1.29413	−	0.747169i	0.314750	−	0.949175i	$-0.398079\pi$
$211$	273.062	−	157.653i	1.29413	−	0.747169i	0.979384	+	0.202006i	$0.0647460\pi$
$212$	−40.8485	+	26.8674i	−0.192682	+	0.126733i
$213$		0			0
$214$	−5.46918	−	18.2678i	−0.0255569	−	0.0853637i
$215$			184.290i			0.857162i
$216$		0			0
$217$	−2.12136			−0.00977583
$218$	−98.4852	+	29.4854i	−0.451767	+	0.135254i
$219$		0			0
$220$	121.340	+	184.482i	0.551544	+	0.838554i
$221$	−67.7981	−	117.430i	−0.306779	−	0.531357i
$222$		0			0
$223$	25.8734	+	14.9380i	0.116024	+	0.0669865i	0.556889	−	0.830587i	$-0.311995\pi$
$223$	25.8734	+	14.9380i	0.116024	+	0.0669865i	−0.440865	+	0.897573i	$0.645328\pi$
$224$	−40.8005	+	54.8090i	−0.182145	+	0.244683i
$225$		0			0
$226$	2.66219	+	2.51161i	0.0117796	+	0.0111133i
$227$	−307.799	−	177.708i	−1.35594	−	0.782855i	−0.366870	−	0.930272i	$-0.619571\pi$
$227$	−307.799	−	177.708i	−1.35594	−	0.782855i	−0.989074	+	0.147418i	$0.952904\pi$
$228$		0			0
$229$	−44.0925	−	76.3705i	−0.192544	−	0.333496i	0.753549	−	0.657392i	$-0.228340\pi$
$229$	−44.0925	−	76.3705i	−0.192544	−	0.333496i	−0.946093	+	0.323896i	$0.895007\pi$
$230$	−347.280	−	82.3039i	−1.50991	−	0.357843i
$231$		0			0
$232$	−52.1004	−	143.134i	−0.224571	−	0.616958i
$233$	251.720			1.08034			0.540172	−	0.841555i	$-0.318359\pi$
$233$	251.720			1.08034			0.540172	+	0.841555i	$0.318359\pi$
$234$		0			0
$235$		−	152.116i		−	0.647303i
$236$	−101.839	+	202.787i	−0.431523	+	0.859266i
$237$		0			0
$238$	−60.8269	−	14.4157i	−0.255575	−	0.0605703i
$239$	−123.211	+	71.1356i	−0.515525	+	0.297639i	−0.735102	−	0.677957i	$-0.762866\pi$
$239$	−123.211	+	71.1356i	−0.515525	+	0.297639i	0.219577	+	0.975595i	$0.429532\pi$
$240$		0			0
$241$	28.5164	−	49.3918i	0.118325	−	0.204945i	−0.800779	−	0.598960i	$-0.795581\pi$
$241$	28.5164	−	49.3918i	0.118325	−	0.204945i	0.919104	+	0.394015i	$0.128914\pi$
$242$	−55.6021	−	52.4571i	−0.229761	−	0.216765i
$243$		0			0
$244$	17.1598	+	294.544i	0.0703272	+	1.20715i
$245$	−97.2096	+	168.372i	−0.396774	+	0.687233i
$246$		0			0
$247$	277.391	−	160.152i	1.12304	−	0.648388i
$248$	1.37996	−	7.82724i	0.00556437	−	0.0315615i
$249$		0			0
$250$	258.678	−	77.4453i	1.03471	−	0.309781i
$251$			0.579617i			0.00230923i	0.999999	+	0.00115462i	$0.000367526\pi$
$251$			0.579617i			0.00230923i	−0.999999	+	0.00115462i	$0.999632\pi$
$252$		0			0
$253$	514.704			2.03440
$254$	26.7660	+	89.4021i	0.105378	+	0.351977i
$255$		0			0
$256$	−175.689	−	186.197i	−0.686287	−	0.727331i
$257$	159.160	+	275.674i	0.619301	+	1.07266i	0.989614	+	0.143753i	$0.0459171\pi$
$257$	159.160	+	275.674i	0.619301	+	1.07266i	−0.370313	+	0.928907i	$0.620750\pi$
$258$		0			0
$259$	−122.834	−	70.9182i	−0.474262	−	0.273816i
$260$	9.42778	+	161.825i	0.0362607	+	0.622405i
$261$		0			0
$262$	−159.424	+	168.983i	−0.608490	+	0.644972i
$263$	−270.344	−	156.083i	−1.02792	−	0.593472i	−0.111535	−	0.993761i	$-0.535577\pi$
$263$	−270.344	−	156.083i	−1.02792	−	0.593472i	−0.916389	+	0.400288i	$0.868910\pi$
$264$		0			0
$265$	26.7367	+	46.3094i	0.100893	+	0.174752i
$266$	34.0526	−	143.684i	0.128017	−	0.540167i
$267$		0			0
$268$	−170.884	+	340.271i	−0.637627	+	1.26967i
$269$	−480.302			−1.78551			−0.892755	−	0.450542i	$-0.851231\pi$
$269$	−480.302			−1.78551			−0.892755	+	0.450542i	$0.851231\pi$
$270$		0			0
$271$			457.090i			1.68668i	0.537381	+	0.843340i	$0.319414\pi$
$271$			457.090i			1.68668i	−0.537381	+	0.843340i	$0.680586\pi$
$272$	92.7587	−	215.057i	0.341025	−	0.790652i
$273$		0			0
$274$	49.7703	−	210.005i	0.181644	−	0.766441i
$275$	−64.0490	+	36.9787i	−0.232905	+	0.134468i
$276$		0			0
$277$	85.6037	−	148.270i	0.309039	−	0.535271i	−0.669114	−	0.743160i	$-0.733326\pi$
$277$	85.6037	−	148.270i	0.309039	−	0.535271i	0.978152	+	0.207889i	$0.0666594\pi$
$278$	−206.048	+	218.402i	−0.741181	+	0.785618i
$279$		0			0
$280$	57.2478	+	48.0343i	0.204456	+	0.171551i
$281$	19.9973	−	34.6363i	0.0711647	−	0.123261i	−0.828247	−	0.560363i	$-0.810662\pi$
$281$	19.9973	−	34.6363i	0.0711647	−	0.123261i	0.899412	+	0.437102i	$0.143995\pi$
$282$		0			0
$283$	−338.527	+	195.449i	−1.19621	+	0.690632i	−0.959708	−	0.281000i	$-0.909334\pi$
$283$	−338.527	+	195.449i	−1.19621	+	0.690632i	−0.236501	+	0.971631i	$0.576001\pi$
$284$	−166.091	−	252.520i	−0.584826	−	0.889155i
$285$		0			0
$286$	−67.0486	−	223.951i	−0.234436	−	0.783047i
$287$		−	55.2748i		−	0.192595i
$288$		0			0
$289$	−74.7271			−0.258571
$290$	−159.595	+	47.7810i	−0.550328	+	0.164762i
$291$		0			0
$292$	−189.548	+	124.672i	−0.649138	+	0.426959i
$293$	−251.725	−	436.001i	−0.859131	−	1.48806i	−0.872759	−	0.488152i	$-0.837671\pi$
$293$	−251.725	−	436.001i	−0.859131	−	1.48806i	0.0136273	−	0.999907i	$-0.495662\pi$
$294$		0			0
$295$	214.934	+	124.092i	0.728591	+	0.420652i
$296$	341.574	−	407.092i	1.15397	−	1.37531i
$297$		0			0
$298$	11.1030	+	10.4750i	0.0372585	+	0.0351511i
$299$	327.229	+	188.926i	1.09441	+	0.631859i
$300$		0			0
$301$	−44.9740	−	77.8972i	−0.149415	−	0.258795i
$302$	412.638	+	97.7936i	1.36635	+	0.323820i
$303$		0			0
$304$	508.006	+	219.113i	1.67107	+	0.720768i
$305$	322.689			1.05800
$306$		0			0
$307$		−	103.154i		−	0.336006i	−0.985786	−	0.168003i	$-0.946268\pi$
$307$		−	103.154i		−	0.336006i	0.985786	−	0.168003i	$-0.0537318\pi$
$308$	−96.3098	−	48.3667i	−0.312694	−	0.157035i
$309$		0			0
$310$	−8.45838	−	2.00460i	−0.0272851	−	0.00646646i
$311$	396.709	−	229.040i	1.27559	−	0.736463i	0.299557	−	0.954078i	$-0.403161\pi$
$311$	396.709	−	229.040i	1.27559	−	0.736463i	0.976035	+	0.217615i	$0.0698277\pi$
$312$		0			0
$313$	−9.31582	+	16.1355i	−0.0297630	+	0.0515510i	−0.880523	−	0.474003i	$-0.842809\pi$
$313$	−9.31582	+	16.1355i	−0.0297630	+	0.0515510i	0.850760	+	0.525554i	$0.176142\pi$
$314$	−89.1934	−	84.1483i	−0.284055	−	0.267988i
$315$		0			0
$316$	297.767	−	17.3476i	0.942300	−	0.0548974i
$317$	−107.895	+	186.880i	−0.340363	+	0.589527i	−0.984500	−	0.175384i	$-0.943883\pi$
$317$	−107.895	+	186.880i	−0.340363	+	0.589527i	0.644137	+	0.764910i	$0.277217\pi$
$318$		0			0
$319$	208.066	−	120.127i	0.652246	−	0.376574i
$320$	−214.474	+	179.982i	−0.670232	+	0.562445i
$321$		0			0
$322$	166.877	−	49.9610i	0.518250	−	0.155158i
$323$			506.152i			1.56704i
$324$		0			0
$325$	−54.2932			−0.167056
$326$	14.5278	+	48.5248i	0.0445638	+	0.148849i
$327$		0			0
$328$	203.949	+	35.9569i	0.621797	+	0.109625i
$329$	37.1224	+	64.2978i	0.112834	+	0.195434i
$330$		0			0
$331$	215.753	+	124.565i	0.651822	+	0.376329i	0.789154	−	0.614196i	$-0.210519\pi$
$331$	215.753	+	124.565i	0.651822	+	0.376329i	−0.137332	+	0.990525i	$0.543853\pi$
$332$	261.526	−	15.2362i	0.787727	−	0.0458922i
$333$		0			0
$334$	190.562	−	201.987i	0.570546	−	0.604752i
$335$	360.655	+	208.224i	1.07658	+	0.621564i
$336$		0			0
$337$	135.945	+	235.464i	0.403398	+	0.698705i	0.994134	−	0.108160i	$-0.0344958\pi$
$337$	135.945	+	235.464i	0.403398	+	0.698705i	−0.590736	+	0.806865i	$0.701162\pi$
$338$	−38.3695	+	161.899i	−0.113519	+	0.478992i
$339$		0			0
$340$	−228.910	−	114.958i	−0.673264	−	0.338113i
$341$	12.5362			0.0367630
$342$		0			0
$343$		−	199.519i		−	0.581688i
$344$	316.676	−	115.269i	0.920570	−	0.335084i
$345$		0			0
$346$	−41.6017	+	175.538i	−0.120236	+	0.507334i
$347$	280.781	−	162.109i	0.809169	−	0.467174i	−0.0374985	−	0.999297i	$-0.511939\pi$
$347$	280.781	−	162.109i	0.809169	−	0.467174i	0.846667	+	0.532123i	$0.178606\pi$
$348$		0			0
$349$	50.5198	−	87.5029i	0.144756	−	0.250725i	−0.784526	−	0.620096i	$-0.787094\pi$
$349$	50.5198	−	87.5029i	0.144756	−	0.250725i	0.929282	+	0.369371i	$0.120427\pi$
$350$	−17.1764	+	18.2062i	−0.0490755	+	0.0520178i
$351$		0			0
$352$	241.111	−	323.895i	0.684974	−	0.920155i
$353$	−75.9329	+	131.520i	−0.215107	+	0.372577i	−0.953306	−	0.302007i	$-0.902343\pi$
$353$	−75.9329	+	131.520i	−0.215107	+	0.372577i	0.738198	+	0.674584i	$0.235677\pi$
$354$		0			0
$355$	−286.278	+	165.283i	−0.806418	+	0.465586i
$356$	501.454	−	329.823i	1.40858	−	0.926468i
$357$		0			0
$358$	23.9266	+	79.9181i	0.0668340	+	0.223235i
$359$		−	594.808i		−	1.65685i	−0.560102	−	0.828424i	$-0.689238\pi$
$359$		−	594.808i		−	1.65685i	0.560102	−	0.828424i	$-0.310762\pi$
$360$		0			0
$361$	−834.626			−2.31198
$362$	−162.209	+	48.5637i	−0.448092	+	0.134154i
$363$		0			0
$364$	−43.4768	−	66.1010i	−0.119442	−	0.181596i
$365$	124.066	+	214.888i	0.339907	+	0.588736i
$366$		0			0
$367$	−151.089	−	87.2311i	−0.411686	−	0.237687i	0.279828	−	0.960050i	$-0.409723\pi$
$367$	−151.089	−	87.2311i	−0.411686	−	0.237687i	−0.691514	+	0.722363i	$0.743056\pi$
$368$	75.7878	+	648.230i	0.205945	+	1.76150i
$369$		0			0
$370$	−422.755	−	398.842i	−1.14258	−	1.07795i
$371$	−22.6026	−	13.0496i	−0.0609235	−	0.0351742i
$372$		0			0
$373$	−144.383	−	250.078i	−0.387085	−	0.670452i	0.604971	−	0.796248i	$-0.293185\pi$
$373$	−144.383	−	250.078i	−0.387085	−	0.670452i	−0.992056	+	0.125796i	$0.959851\pi$
$374$	359.457	+	85.1900i	0.961116	+	0.227781i
$375$		0			0
$376$	−261.390	+	95.1453i	−0.695187	+	0.253046i
$377$	176.374			0.467837
$378$		0			0
$379$			260.534i			0.687425i	0.939075	+	0.343713i	$0.111685\pi$
$379$			260.534i			0.687425i	−0.939075	+	0.343713i	$0.888315\pi$
$380$	271.553	−	540.727i	0.714613	−	1.42297i
$381$		0			0
$382$	342.748	+	81.2300i	0.897247	+	0.212644i
$383$	−303.817	+	175.409i	−0.793257	+	0.457987i	−0.841108	−	0.540867i	$-0.818096\pi$
$383$	−303.817	+	175.409i	−0.793257	+	0.457987i	0.0478509	+	0.998854i	$0.484763\pi$
$384$		0			0
$385$	−58.9354	+	102.079i	−0.153079	+	0.265141i
$386$	−484.213	−	456.824i	−1.25444	−	1.18348i
$387$		0			0
$388$	−26.2618	−	450.777i	−0.0676851	−	1.16180i
$389$	16.5571	−	28.6777i	0.0425632	−	0.0737216i	−0.843959	−	0.536408i	$-0.819781\pi$
$389$	16.5571	−	28.6777i	0.0425632	−	0.0737216i	0.886522	+	0.462686i	$0.153114\pi$
$390$		0			0
$391$	−517.097	+	298.546i	−1.32250	+	0.763545i
$392$	350.126	+	61.7282i	0.893179	+	0.157470i
$393$		0			0
$394$	262.944	−	78.7224i	0.667370	−	0.199803i
$395$		−	326.220i		−	0.825872i
$396$		0			0
$397$	357.151			0.899625			0.449813	−	0.893123i	$-0.351491\pi$
$397$	357.151			0.899625			0.449813	+	0.893123i	$0.351491\pi$
$398$	164.146	+	548.270i	0.412427	+	1.37756i
$399$		0			0
$400$	−56.0028	−	75.2199i	−0.140007	−	0.188050i
$401$	159.123	+	275.608i	0.396814	+	0.687303i	0.993331	−	0.115298i	$-0.0367823\pi$
$401$	159.123	+	275.608i	0.396814	+	0.687303i	−0.596517	+	0.802601i	$0.703449\pi$
$402$		0			0
$403$	7.97003	+	4.60150i	0.0197768	+	0.0114181i
$404$	−10.2226	−	175.469i	−0.0253035	−	0.434328i
$405$		0			0
$406$	55.7986	−	59.1439i	0.137435	−	0.145675i
$407$	725.889	+	419.092i	1.78351	+	1.02971i
$408$		0			0
$409$	−256.803	−	444.796i	−0.627880	−	1.08752i	−0.987976	−	0.154605i	$-0.950590\pi$
$409$	−256.803	−	444.796i	−0.627880	−	1.08752i	0.360097	−	0.932915i	$-0.382744\pi$
$410$	52.2327	−	220.395i	0.127397	−	0.537548i
$411$		0			0
$412$	−137.693	+	274.180i	−0.334206	+	0.665485i
$413$	−121.134			−0.293302
$414$		0			0
$415$		−	286.515i		−	0.690399i
$416$	272.177	−	117.418i	0.654272	−	0.282256i
$417$		0			0
$418$	−201.235	+	849.105i	−0.481422	+	2.03135i
$419$	−62.7466	+	36.2268i	−0.149753	+	0.0864601i	−0.573004	−	0.819552i	$-0.694222\pi$
$419$	−62.7466	+	36.2268i	−0.149753	+	0.0864601i	0.423251	+	0.906012i	$0.360889\pi$
$420$		0			0
$421$	−315.617	+	546.665i	−0.749685	+	1.29849i	0.198289	+	0.980144i	$0.436462\pi$
$421$	−315.617	+	546.665i	−0.749685	+	1.29849i	−0.947974	+	0.318349i	$0.896872\pi$
$422$	−432.748	+	458.693i	−1.02547	+	1.08695i
$423$		0			0
$424$	62.8529	−	74.9088i	0.148238	−	0.176672i
$425$	42.8978	−	74.3012i	0.100936	−	0.174826i
$426$		0			0
$427$	−136.397	+	78.7488i	−0.319431	+	0.184423i
$428$	20.9576	+	31.8634i	0.0489664	+	0.0744473i
$429$		0			0
$430$	−105.713	−	353.095i	−0.245843	−	0.821150i
$431$		−	73.3222i		−	0.170121i	−0.996376	−	0.0850606i	$-0.972892\pi$
$431$		−	73.3222i		−	0.170121i	0.996376	−	0.0850606i	$-0.0271084\pi$
$432$		0			0
$433$	−575.286			−1.32860			−0.664302	−	0.747464i	$-0.731271\pi$
$433$	−575.286			−1.32860			−0.664302	+	0.747464i	$0.731271\pi$
$434$	4.06446	−	1.21686i	0.00936512	−	0.00280381i
$435$		0			0
$436$	171.782	−	112.986i	0.393995	−	0.259143i
$437$	−705.221	−	1221.48i	−1.61378	−	2.79515i
$438$		0			0
$439$	206.677	+	119.325i	0.470791	+	0.271811i	0.716571	−	0.697514i	$-0.245711\pi$
$439$	206.677	+	119.325i	0.470791	+	0.271811i	−0.245780	+	0.969326i	$0.579044\pi$
$440$	−338.307	−	283.860i	−0.768879	−	0.645135i
$441$		0			0
$442$	197.260	+	186.102i	0.446289	+	0.421045i
$443$	45.3661	+	26.1921i	0.102407	+	0.0591244i	0.550329	−	0.834948i	$-0.314502\pi$
$443$	45.3661	+	26.1921i	0.102407	+	0.0591244i	−0.447922	+	0.894073i	$0.647836\pi$
$444$		0			0
$445$	−328.219	−	568.492i	−0.737571	−	1.27751i
$446$	−58.1414	−	13.7793i	−0.130362	−	0.0308953i
$447$		0			0
$448$	46.7330	−	128.417i	0.104315	−	0.286644i
$449$	566.091			1.26078			0.630391	−	0.776277i	$-0.282894\pi$
$449$	566.091			1.26078			0.630391	+	0.776277i	$0.282894\pi$
$450$		0			0
$451$			326.648i			0.724274i
$452$	−6.54141	−	3.28509i	−0.0144721	−	0.00726790i
$453$		0			0
$454$	691.673	+	163.924i	1.52351	+	0.361066i
$455$	−74.9378	+	43.2654i	−0.164698	+	0.0950887i
$456$		0			0
$457$	17.1799	−	29.7564i	0.0375927	−	0.0651125i	−0.846617	−	0.532203i	$-0.821364\pi$
$457$	17.1799	−	29.7564i	0.0375927	−	0.0651125i	0.884210	+	0.467090i	$0.154698\pi$
$458$	128.288	+	121.032i	0.280105	+	0.264261i
$459$		0			0
$460$	712.590	−	41.5148i	1.54911	−	0.0902496i
$461$	−136.272	+	236.031i	−0.295602	+	0.511997i	−0.975125	−	0.221657i	$-0.928853\pi$
$461$	−136.272	+	236.031i	−0.295602	+	0.511997i	0.679523	+	0.733654i	$0.262187\pi$
$462$		0			0
$463$	−489.759	+	282.763i	−1.05780	+	0.610719i	−0.924822	−	0.380401i	$-0.875786\pi$
$463$	−489.759	+	282.763i	−1.05780	+	0.610719i	−0.132974	+	0.991120i	$0.542453\pi$
$464$	181.928	+	244.356i	0.392086	+	0.526629i
$465$		0			0
$466$	−482.289	+	144.392i	−1.03496	+	0.309854i
$467$		−	893.925i		−	1.91419i	−0.289780	−	0.957093i	$-0.593582\pi$
$467$		−	893.925i		−	1.91419i	0.289780	−	0.957093i	$-0.406418\pi$
$468$		0			0
$469$	−203.259			−0.433389
$470$	87.2572	+	291.451i	0.185654	+	0.620108i
$471$		0			0
$472$	78.7988	−	446.952i	0.166947	−	0.946931i
$473$	265.774	+	460.335i	0.561891	+	0.973224i
$474$		0			0
$475$	175.513	+	101.333i	0.369502	+	0.213332i
$476$	124.812	−	7.27142i	0.262210	−	0.0152761i
$477$		0			0
$478$	195.263	−	206.970i	0.408501	−	0.432992i
$479$	−467.745	−	270.053i	−0.976504	−	0.563785i	−0.0752909	−	0.997162i	$-0.523989\pi$
$479$	−467.745	−	270.053i	−0.976504	−	0.563785i	−0.901213	+	0.433377i	$0.857322\pi$
$480$		0			0
$481$	307.662	+	532.886i	0.639630	+	1.10787i
$482$	−26.3044	+	110.991i	−0.0545735	+	0.230272i
$483$		0			0
$484$	136.623	+	68.6118i	0.282278	+	0.141760i
$485$	−493.850			−1.01825
$486$		0			0
$487$			518.681i			1.06505i	0.846413	+	0.532526i	$0.178757\pi$
$487$			518.681i			1.06505i	−0.846413	+	0.532526i	$0.821243\pi$
$488$	−201.835	−	554.496i	−0.413595	−	1.13626i
$489$		0			0
$490$	89.6694	−	378.358i	0.182999	−	0.772159i
$491$	−130.195	+	75.1683i	−0.265163	+	0.153092i	−0.626688	−	0.779271i	$-0.715590\pi$
$491$	−130.195	+	75.1683i	−0.265163	+	0.153092i	0.361524	+	0.932363i	$0.382256\pi$
$492$		0			0
$493$	−139.356	+	241.371i	−0.282669	+	0.489597i
$494$	−439.608	+	465.964i	−0.889894	+	0.943247i
$495$		0			0
$496$	1.84589	+	15.7884i	0.00372156	+	0.0318314i
$497$	80.6711	−	139.726i	0.162316	−	0.281140i
$498$		0			0
$499$	265.749	−	153.430i	0.532564	−	0.307476i	−0.209496	−	0.977810i	$-0.567182\pi$
$499$	265.749	−	153.430i	0.532564	−	0.307476i	0.742060	+	0.670334i	$0.233849\pi$
$500$	−451.196	+	296.767i	−0.902393	+	0.593533i
$501$		0			0
$502$	−0.332481	−	1.11053i	−0.000662312	−	0.00221221i
$503$			731.474i			1.45422i	0.686520	+	0.727111i	$0.259137\pi$
$503$			731.474i			1.45422i	−0.686520	+	0.727111i	$0.740863\pi$
$504$		0			0
$505$	−192.235			−0.380664
$506$	−986.160	+	295.245i	−1.94893	+	0.583489i
$507$		0			0
$508$	−102.566	−	155.939i	−0.201901	−	0.306966i
$509$	−29.6107	−	51.2873i	−0.0581743	−	0.100761i	0.835472	−	0.549534i	$-0.185195\pi$
$509$	−29.6107	−	51.2873i	−0.0581743	−	0.100761i	−0.893646	+	0.448773i	$0.851861\pi$
$510$		0			0
$511$	−104.883	−	60.5540i	−0.205250	−	0.118501i
$512$	443.423	+	255.969i	0.866060	+	0.499939i
$513$		0			0
$514$	−463.079	−	436.886i	−0.900933	−	0.849973i
$515$	290.604	+	167.780i	0.564280	+	0.325787i
$516$		0			0
$517$	−219.375	−	379.969i	−0.424323	−	0.734950i
$518$	276.027	+	65.4173i	0.532871	+	0.126288i
$519$		0			0
$520$	−110.890	−	304.645i	−0.213250	−	0.585856i
$521$	689.100			1.32265			0.661324	−	0.750100i	$-0.269995\pi$
$521$	689.100			1.32265			0.661324	+	0.750100i	$0.269995\pi$
$522$		0			0
$523$			431.237i			0.824544i	0.911061	+	0.412272i	$0.135265\pi$
$523$			431.237i			0.824544i	−0.911061	+	0.412272i	$0.864735\pi$
$524$	208.521	−	415.216i	0.397941	−	0.792396i
$525$		0			0
$526$	607.505	+	143.976i	1.15495	+	0.273719i
$527$	−12.5945	+	7.27142i	−0.0238984	+	0.0137978i
$528$		0			0
$529$	567.427	−	982.812i	1.07264	−	1.85787i
$530$	−77.7910	−	73.3908i	−0.146775	−	0.138473i
$531$		0			0
$532$	17.1764	+	294.829i	0.0322865	+	0.554190i
$533$	−119.898	+	207.670i	−0.224950	+	0.389625i
$534$		0			0
$535$	36.1232	−	20.8557i	0.0675199	−	0.0389827i
$536$	132.222	−	749.974i	0.246684	−	1.39920i
$537$		0			0
$538$	920.247	−	275.512i	1.71050	−	0.512103i
$539$			560.765i			1.04038i
$540$		0			0
$541$	99.8398			0.184547			0.0922734	−	0.995734i	$-0.470587\pi$
$541$	99.8398			0.184547			0.0922734	+	0.995734i	$0.470587\pi$
$542$	−262.197	−	875.773i	−0.483758	−	1.61582i
$543$		0			0
$544$	−54.3619	+	465.253i	−0.0999299	+	0.855244i
$545$	−112.437	−	194.747i	−0.206306	−	0.357333i
$546$		0			0
$547$	−413.671	−	238.833i	−0.756254	−	0.436624i	0.0716949	−	0.997427i	$-0.477159\pi$
$547$	−413.671	−	238.833i	−0.756254	−	0.436624i	−0.827949	+	0.560803i	$0.810493\pi$
$548$	25.1046	+	430.913i	0.0458113	+	0.786338i
$549$		0			0
$550$	101.504	−	107.590i	0.184554	−	0.195618i
$551$	−570.164	−	329.184i	−1.03478	−	0.597431i
$552$		0			0
$553$	79.6104	+	137.889i	0.143961	+	0.249348i
$554$	−78.9637	+	333.186i	−0.142534	+	0.601418i
$555$		0			0
$556$	269.503	−	536.646i	0.484718	−	0.965191i
$557$	227.316			0.408108			0.204054	−	0.978960i	$-0.434588\pi$
$557$	227.316			0.408108			0.204054	+	0.978960i	$0.434588\pi$
$558$		0			0
$559$			390.218i			0.698064i
$560$	−137.239	−	59.1940i	−0.245069	−	0.105704i
$561$		0			0
$562$	−18.4462	+	77.8332i	−0.0328224	+	0.138493i
$563$	−671.826	+	387.879i	−1.19330	+	0.688950i	−0.959053	−	0.283227i	$-0.908595\pi$
$563$	−671.826	+	387.879i	−1.19330	+	0.688950i	−0.234244	+	0.972178i	$0.575262\pi$
$564$		0			0
$565$	−4.00292	+	6.93326i	−0.00708481	+	0.0122713i
$566$	536.496	−	568.661i	0.947872	−	1.00470i
$567$		0			0
$568$	463.076	+	388.549i	0.815275	+	0.684064i
$569$	−477.933	+	827.803i	−0.839952	+	1.45484i	0.0499825	+	0.998750i	$0.484083\pi$
$569$	−477.933	+	827.803i	−0.839952	+	1.45484i	−0.889934	+	0.456089i	$0.849250\pi$
$570$		0			0
$571$	754.720	−	435.738i	1.32175	−	0.763113i	0.337743	−	0.941238i	$-0.390337\pi$
$571$	754.720	−	435.738i	1.32175	−	0.763113i	0.984008	+	0.178125i	$0.0570032\pi$
$572$	256.927	+	390.625i	0.449172	+	0.682910i
$573$		0			0
$574$	31.7068	+	105.905i	0.0552384	+	0.184504i
$575$			239.078i			0.415787i
$576$		0			0
$577$	241.573			0.418671			0.209335	−	0.977844i	$-0.432870\pi$
$577$	241.573			0.418671			0.209335	+	0.977844i	$0.432870\pi$
$578$	143.175	−	42.8651i	0.247708	−	0.0741610i
$579$		0			0
$580$	278.372	−	183.094i	0.479951	−	0.315680i
$581$	69.9210	+	121.107i	0.120346	+	0.208445i
$582$		0			0
$583$	133.571	+	77.1170i	0.229109	+	0.132276i
$584$	291.655	−	347.598i	0.499410	−	0.595202i
$585$		0			0
$586$	732.399	+	690.972i	1.24983	+	1.17913i
$587$	−577.552	−	333.450i	−0.983905	−	0.568058i	−0.0804579	−	0.996758i	$-0.525638\pi$
$587$	−577.552	−	333.450i	−0.983905	−	0.568058i	−0.903447	+	0.428700i	$0.858972\pi$
$588$		0			0
$589$	−17.1764	−	29.7505i	−0.0291620	−	0.0505101i
$590$	−482.991	−	114.467i	−0.818629	−	0.194012i
$591$		0			0
$592$	−420.931	+	975.912i	−0.711032	+	1.64850i
$593$	−207.914			−0.350613			−0.175307	−	0.984514i	$-0.556092\pi$
$593$	−207.914			−0.350613			−0.175307	+	0.984514i	$0.556092\pi$
$594$		0			0
$595$		−	136.738i		−	0.229812i
$596$	−27.2818	−	13.7009i	−0.0457749	−	0.0229881i
$597$		0			0
$598$	−735.335	−	174.272i	−1.22966	−	0.291424i
$599$	−283.333	+	163.582i	−0.473010	+	0.273092i	−0.717499	−	0.696560i	$-0.754713\pi$
$599$	−283.333	+	163.582i	−0.473010	+	0.273092i	0.244489	+	0.969652i	$0.421380\pi$
$600$		0			0
$601$	−25.0218	+	43.3391i	−0.0416337	+	0.0721116i	−0.886091	−	0.463511i	$-0.846590\pi$
$601$	−25.0218	+	43.3391i	−0.0416337	+	0.0721116i	0.844458	+	0.535622i	$0.179923\pi$
$602$	130.853	+	123.451i	0.217363	+	0.205068i
$603$		0			0
$604$	−846.700	+	49.3279i	−1.40182	+	0.0816687i
$605$	83.6043	−	144.807i	0.138189	−	0.239350i
$606$		0			0
$607$	359.185	−	207.375i	0.591737	−	0.341640i	−0.174047	−	0.984737i	$-0.555684\pi$
$607$	359.185	−	207.375i	0.591737	−	0.341640i	0.765784	+	0.643098i	$0.222351\pi$
$608$	−1099.01	−	128.413i	−1.80759	−	0.211205i
$609$		0			0
$610$	−618.264	+	185.101i	−1.01355	+	0.303445i
$611$		−	322.093i		−	0.527158i
$612$		0			0
$613$	−287.998			−0.469817			−0.234909	−	0.972017i	$-0.575479\pi$
$613$	−287.998			−0.469817			−0.234909	+	0.972017i	$0.575479\pi$
$614$	59.1713	+	197.640i	0.0963701	+	0.321890i
$615$		0			0
$616$	212.271	+	37.4240i	0.344596	+	0.0607533i
$617$	127.843	+	221.430i	0.207201	+	0.358882i	0.950832	−	0.309708i	$-0.100231\pi$
$617$	127.843	+	221.430i	0.207201	+	0.358882i	−0.743631	+	0.668590i	$0.766898\pi$
$618$		0			0
$619$	−8.60391	−	4.96747i	−0.0138997	−	0.00802499i	0.493034	−	0.870010i	$-0.335888\pi$
$619$	−8.60391	−	4.96747i	−0.0138997	−	0.00802499i	−0.506934	+	0.861985i	$0.669221\pi$
$620$	17.3559	−	1.01114i	0.0279934	−	0.00163087i
$621$		0			0
$622$	−628.702	+	666.396i	−1.01078	+	1.07138i
$623$	277.469	+	160.197i	0.445375	+	0.257138i
$624$		0			0
$625$	222.059	+	384.618i	0.355295	+	0.615389i
$626$	8.59322	−	36.2589i	0.0137272	−	0.0579216i
$627$		0			0
$628$	219.162	+	110.063i	0.348983	+	0.175259i
$629$	−972.352			−1.54587
$630$		0			0
$631$			784.610i			1.24344i	0.783240	+	0.621719i	$0.213566\pi$
$631$			784.610i			1.24344i	−0.783240	+	0.621719i	$0.786434\pi$
$632$	−560.562	+	204.043i	−0.886966	+	0.322853i
$633$		0			0
$634$	99.5261	−	419.948i	0.156981	−	0.662379i
$635$	−176.786	+	102.067i	−0.278402	+	0.160736i
$636$		0			0
$637$	−205.833	+	356.513i	−0.323129	+	0.559676i
$638$	−329.742	+	349.512i	−0.516838	+	0.547825i
$639$		0			0
$640$	307.685	−	467.868i	0.480758	−	0.731045i
$641$	585.512	−	1014.14i	0.913436	−	1.58212i	0.104261	−	0.994550i	$-0.466752\pi$
$641$	585.512	−	1014.14i	0.913436	−	1.58212i	0.809175	−	0.587567i	$-0.199914\pi$
$642$		0			0
$643$	−466.249	+	269.189i	−0.725115	+	0.418645i	−0.816632	−	0.577158i	$-0.804162\pi$
$643$	−466.249	+	269.189i	−0.725115	+	0.418645i	0.0915175	+	0.995803i	$0.470828\pi$
$644$	−291.073	+	191.448i	−0.451976	+	0.297279i
$645$		0			0
$646$	−290.340	−	969.775i	−0.449443	−	1.50120i
$647$		−	170.070i		−	0.262860i	−0.991325	−	0.131430i	$-0.958043\pi$
$647$		−	170.070i		−	0.262860i	0.991325	−	0.131430i	$-0.0419568\pi$
$648$		0			0
$649$	715.842			1.10299
$650$	104.024	−	31.1438i	0.160038	−	0.0479135i
$651$		0			0
$652$	−55.6698	−	84.6389i	−0.0853831	−	0.129814i
$653$	−79.1035	−	137.011i	−0.121139	−	0.209818i	0.799078	−	0.601227i	$-0.205321\pi$
$653$	−79.1035	−	137.011i	−0.121139	−	0.209818i	−0.920217	+	0.391409i	$0.871988\pi$
$654$		0			0
$655$	−440.088	−	254.085i	−0.671891	−	0.387916i
$656$	−411.388	+	48.0973i	−0.627115	+	0.0733191i
$657$		0			0
$658$	−108.008	−	101.899i	−0.164146	−	0.154861i
$659$	227.314	+	131.240i	0.344938	+	0.199150i	0.662453	−	0.749103i	$-0.269515\pi$
$659$	227.314	+	131.240i	0.344938	+	0.199150i	−0.317516	+	0.948253i	$0.602849\pi$
$660$		0			0
$661$	133.649	+	231.487i	0.202192	+	0.350207i	0.949234	−	0.314569i	$-0.101860\pi$
$661$	133.649	+	231.487i	0.202192	+	0.350207i	−0.747042	+	0.664776i	$0.768527\pi$
$662$	−484.830	−	114.903i	−0.732372	−	0.173569i
$663$		0			0
$664$	−492.336	+	179.209i	−0.741471	+	0.269893i
$665$	323.001			0.485716
$666$		0			0
$667$		−	776.656i		−	1.16440i
$668$	−249.248	+	496.313i	−0.373126	+	0.742984i
$669$		0			0
$670$	−810.447	−	192.073i	−1.20962	−	0.286676i
$671$	806.040	−	465.367i	1.20125	−	0.693543i
$672$		0			0
$673$	47.8491	−	82.8770i	0.0710982	−	0.123146i	−0.828285	−	0.560307i	$-0.810683\pi$
$673$	47.8491	−	82.8770i	0.0710982	−	0.123146i	0.899383	+	0.437162i	$0.144016\pi$
$674$	−395.534	−	373.161i	−0.586846	−	0.553652i
$675$		0			0
$676$	−19.3539	−	332.204i	−0.0286300	−	0.491427i
$677$	266.057	−	460.825i	0.392995	−	0.680687i	−0.599848	−	0.800114i	$-0.704772\pi$
$677$	266.057	−	460.825i	0.392995	−	0.680687i	0.992843	+	0.119427i	$0.0381057\pi$
$678$		0			0
$679$	208.745	−	120.519i	0.307430	−	0.177495i
$680$	504.528	+	88.9497i	0.741952	+	0.130808i
$681$		0			0
$682$	−24.0190	+	7.19102i	−0.0352185	+	0.0105440i
$683$			622.200i			0.910981i	0.890241	+	0.455491i	$0.150536\pi$
$683$			622.200i			0.910981i	−0.890241	+	0.455491i	$0.849464\pi$
$684$		0			0
$685$	472.089			0.689181
$686$	114.448	+	382.273i	0.166834	+	0.557250i
$687$		0			0
$688$	−540.623	+	402.505i	−0.785789	+	0.585036i
$689$	56.6128	+	98.0562i	0.0821666	+	0.142317i
$690$		0			0
$691$	225.074	+	129.946i	0.325722	+	0.188056i	0.653940	−	0.756546i	$-0.273115\pi$
$691$	225.074	+	129.946i	0.325722	+	0.188056i	−0.328218	+	0.944602i	$0.606448\pi$
$692$	−20.9843	−	360.189i	−0.0303241	−	0.520505i
$693$		0			0
$694$	−444.981	+	471.660i	−0.641183	+	0.679625i
$695$	−568.793	−	328.393i	−0.818407	−	0.472508i
$696$		0			0
$697$	−189.467	−	328.166i	−0.271832	−	0.470826i
$698$	−46.6011	+	196.633i	−0.0667638	+	0.281708i
$699$		0			0
$700$	22.4661	−	44.7355i	0.0320945	−	0.0639078i
$701$	−1233.75			−1.75998			−0.879992	−	0.474988i	$-0.842452\pi$
$701$	−1233.75			−1.75998			−0.879992	+	0.474988i	$0.842452\pi$
$702$		0			0
$703$		−	2296.88i		−	3.26725i
$704$	−276.170	+	758.880i	−0.392286	+	1.07795i
$705$		0			0
$706$	70.0430	−	295.545i	0.0992111	−	0.418619i
$707$	81.2557	−	46.9130i	0.114930	−	0.0663550i
$708$		0			0
$709$	−124.002	+	214.778i	−0.174897	+	0.302930i	−0.940126	−	0.340828i	$-0.889293\pi$
$709$	−124.002	+	214.778i	−0.174897	+	0.302930i	0.765229	+	0.643759i	$0.222626\pi$
$710$	453.692	−	480.893i	0.639003	−	0.677315i
$711$		0			0
$712$	−771.580	+	919.577i	−1.08368	+	1.29154i
$713$	20.2625	−	35.0957i	0.0284186	−	0.0492225i
$714$		0			0
$715$	442.846	−	255.677i	0.619365	−	0.357591i
$716$	−91.6854	−	139.396i	−0.128052	−	0.194687i
$717$		0			0
$718$	341.195	+	1139.64i	0.475202	+	1.58724i
$719$		−	925.022i		−	1.28654i	−0.765639	−	0.643270i	$-0.777577\pi$
$719$		−	925.022i		−	1.28654i	0.765639	−	0.643270i	$-0.222423\pi$
$720$		0			0
$721$	−163.780			−0.227157
$722$	1599.12	−	478.759i	2.21485	−	0.663102i
$723$		0			0
$724$	282.932	−	186.094i	0.390790	−	0.257035i
$725$	55.7986	+	96.6459i	0.0769635	+	0.133305i
$726$		0			0
$727$	−611.539	−	353.072i	−0.841182	−	0.485657i	0.0164837	−	0.999864i	$-0.494753\pi$
$727$	−611.539	−	353.072i	−0.841182	−	0.485657i	−0.857666	+	0.514207i	$0.828086\pi$
$728$	121.217	+	101.709i	0.166507	+	0.139710i
$729$		0			0
$730$	−360.972	−	340.554i	−0.494482	−	0.466512i
$731$	−534.020	−	308.317i	−0.730533	−	0.421774i
$732$		0			0
$733$	392.416	+	679.684i	0.535356	+	0.927264i	0.999146	+	0.0413185i	$0.0131558\pi$
$733$	392.416	+	679.684i	0.535356	+	0.927264i	−0.463790	+	0.885945i	$0.653511\pi$
$734$	339.520	+	80.4649i	0.462561	+	0.109625i
$735$		0			0
$736$	−517.046	−	1198.52i	−0.702509	−	1.62842i
$737$	1201.17			1.62980
$738$		0			0
$739$		−	758.298i		−	1.02611i	−0.858355	−	0.513057i	$-0.828513\pi$
$739$		−	758.298i		−	1.02611i	0.858355	−	0.513057i	$-0.171487\pi$
$740$	1038.77	+	521.671i	1.40375	+	0.704960i
$741$		0			0
$742$	50.7916	+	12.0374i	0.0684523	+	0.0162229i
$743$	103.996	−	60.0421i	0.139968	−	0.0808103i	−0.428381	−	0.903598i	$-0.640916\pi$
$743$	103.996	−	60.0421i	0.139968	−	0.0808103i	0.568349	+	0.822788i	$0.307583\pi$
$744$		0			0
$745$	−16.6947	+	28.9161i	−0.0224090	+	0.0388136i
$746$	420.084	+	396.323i	0.563116	+	0.531264i
$747$		0			0
$748$	−737.578	+	42.9706i	−0.986067	+	0.0574473i
$749$	−10.1792	+	17.6310i	−0.0135904	+	0.0235393i
$750$		0			0
$751$	175.822	−	101.511i	0.234117	−	0.135167i	−0.378353	−	0.925661i	$-0.623509\pi$
$751$	175.822	−	101.511i	0.234117	−	0.135167i	0.612470	+	0.790494i	$0.290176\pi$
$752$	446.240	−	332.235i	0.593404	−	0.441802i
$753$		0			0
$754$	−337.929	+	101.172i	−0.448181	+	0.134181i
$755$			927.606i			1.22862i
$756$		0			0
$757$	690.610			0.912298			0.456149	−	0.889903i	$-0.349228\pi$
$757$	690.610			0.912298			0.456149	+	0.889903i	$0.349228\pi$
$758$	−149.448	−	499.177i	−0.197161	−	0.658545i
$759$		0			0
$760$	−210.116	+	1191.79i	−0.276468	+	1.56814i
$761$	574.862	+	995.691i	0.755404	+	1.30840i	0.945173	+	0.326569i	$0.105893\pi$
$761$	574.862	+	995.691i	0.755404	+	1.30840i	−0.189770	+	0.981829i	$0.560774\pi$
$762$		0			0
$763$	95.0517	+	54.8781i	0.124576	+	0.0719241i
$764$	−703.292	+	40.9731i	−0.920540	+	0.0536297i
$765$		0			0
$766$	481.488	−	510.355i	0.628574	−	0.666260i
$767$	455.105	+	262.755i	0.593358	+	0.342575i
$768$		0			0
$769$	317.346	+	549.659i	0.412673	+	0.714771i	0.995181	−	0.0980542i	$-0.0312618\pi$
$769$	317.346	+	549.659i	0.412673	+	0.714771i	−0.582508	+	0.812825i	$0.697929\pi$
$770$	54.3640	−	229.388i	0.0706025	−	0.297906i
$771$		0			0
$772$	1189.78	+	597.509i	1.54117	+	0.773975i
$773$	−267.560			−0.346132			−0.173066	−	0.984910i	$-0.555367\pi$
$773$	−267.560			−0.346132			−0.173066	+	0.984910i	$0.555367\pi$
$774$		0			0
$775$			5.82300i			0.00751355i
$776$	308.892	+	848.612i	0.398057	+	1.09357i
$777$		0			0
$778$	−15.2728	+	64.4432i	−0.0196308	+	0.0828319i
$779$	775.189	−	447.556i	0.995108	−	0.574526i
$780$		0			0
$781$	−476.727	+	825.716i	−0.610406	+	1.05725i
$782$	819.492	−	868.624i	1.04794	−	1.11077i
$783$		0			0
$784$	−706.241	+	82.5701i	−0.900818	+	0.105319i
$785$	134.113	−	232.290i	0.170844	−	0.295911i
$786$		0			0
$787$	−563.164	+	325.143i	−0.715583	+	0.413142i	−0.813125	−	0.582089i	$-0.802235\pi$
$787$	−563.164	+	325.143i	−0.715583	+	0.413142i	0.0975416	+	0.995231i	$0.468902\pi$
$788$	−458.636	+	301.660i	−0.582026	+	0.382817i
$789$		0			0
$790$	187.127	+	625.028i	0.236869	+	0.791175i
$791$		−	3.90748i		−	0.00493993i
$792$		0			0
$793$	683.266			0.861622
$794$	−684.293	+	204.870i	−0.861830	+	0.258022i
$795$		0			0
$796$	−628.998	−	956.313i	−0.790199	−	1.20140i
$797$	503.422	+	871.953i	0.631646	+	1.09404i	0.987215	+	0.159393i	$0.0509538\pi$
$797$	503.422	+	871.953i	0.631646	+	1.09404i	−0.355569	+	0.934650i	$0.615713\pi$
$798$		0			0
$799$	440.790	+	254.490i	0.551677	+	0.318511i
$800$	150.448	+	111.995i	0.188059	+	0.139994i
$801$		0			0
$802$	−462.970	−	436.783i	−0.577269	−	0.544617i
$803$	619.805	+	357.845i	0.771862	+	0.445635i
$804$		0			0
$805$	190.517	+	329.985i	0.236667	+	0.409919i
$806$	−17.9099	−	4.24458i	−0.0222207	−	0.00526622i
$807$		0			0
$808$	120.239	+	330.329i	0.148810	+	0.408824i
$809$	135.483			0.167469			0.0837347	−	0.996488i	$-0.473315\pi$
$809$	135.483			0.167469			0.0837347	+	0.996488i	$0.473315\pi$
$810$		0			0
$811$			86.4723i			0.106624i	0.998578	+	0.0533122i	$0.0169778\pi$
$811$			86.4723i			0.106624i	−0.998578	+	0.0533122i	$0.983022\pi$
$812$	−72.9824	+	145.326i	−0.0898798	+	0.178972i
$813$		0			0
$814$	−1631.19	−	386.585i	−2.00391	−	0.474920i
$815$	−95.9540	+	55.3991i	−0.117735	+	0.0679743i
$816$		0			0
$817$	728.301	−	1261.45i	0.891433	−	1.54401i
$818$	747.172	+	704.909i	0.913413	+	0.861748i
$819$		0			0
$820$	26.3466	+	452.232i	0.0321300	+	0.551503i
$821$	334.340	−	579.094i	0.407235	−	0.705352i	−0.587344	−	0.809338i	$-0.699826\pi$
$821$	334.340	−	579.094i	0.407235	−	0.705352i	0.994579	+	0.103986i	$0.0331596\pi$
$822$		0			0
$823$	710.023	−	409.932i	0.862725	−	0.498095i	−0.00219864	−	0.999998i	$-0.500700\pi$
$823$	710.023	−	409.932i	0.862725	−	0.498095i	0.864924	+	0.501903i	$0.167367\pi$
$824$	106.541	−	604.305i	0.129297	−	0.733380i
$825$		0			0
$826$	232.089	−	69.4849i	0.280980	−	0.0841222i
$827$		−	357.121i		−	0.431827i	−0.976413	−	0.215913i	$-0.930727\pi$
$827$		−	357.121i		−	0.431827i	0.976413	−	0.215913i	$-0.0692729\pi$
$828$		0			0
$829$	257.314			0.310390			0.155195	−	0.987884i	$-0.450399\pi$
$829$	257.314			0.310390			0.155195	+	0.987884i	$0.450399\pi$
$830$	164.351	+	548.956i	0.198014	+	0.661393i
$831$		0			0
$832$	−454.131	+	381.097i	−0.545830	+	0.458050i
$833$	−325.263	−	563.372i	−0.390472	−	0.676317i
$834$		0			0
$835$	526.044	+	303.712i	0.629993	+	0.363726i
$836$	−101.504	−	1742.30i	−0.121417	−	2.08409i
$837$		0			0
$838$	99.4405	−	105.402i	0.118664	−	0.125779i
$839$	580.117	+	334.931i	0.691439	+	0.399203i	0.804151	−	0.594425i	$-0.202620\pi$
$839$	580.117	+	334.931i	0.691439	+	0.399203i	−0.112712	+	0.993628i	$0.535954\pi$
$840$		0			0
$841$	239.235	+	414.368i	0.284465	+	0.492709i
$842$	291.136	−	1228.44i	0.345767	−	1.45896i
$843$		0			0
$844$	566.017	−	1127.08i	0.670637	−	1.33540i
$845$	−363.948			−0.430708
$846$		0			0
$847$			81.6110i			0.0963530i
$848$	−77.4554	+	179.577i	−0.0913389	+	0.211765i
$849$		0			0
$850$	−39.5704	+	166.966i	−0.0465534	+	0.196431i
$851$	2346.54	−	1354.78i	2.75739	−	1.59198i
$852$		0			0
$853$	444.254	−	769.470i	0.520813	−	0.902075i	−0.478894	−	0.877873i	$-0.658962\pi$
$853$	444.254	−	769.470i	0.520813	−	0.902075i	0.999707	−	0.0242024i	$-0.00770462\pi$
$854$	216.161	−	229.121i	0.253116	−	0.268291i
$855$		0			0
$856$	−58.4318	−	49.0278i	−0.0682615	−	0.0572755i
$857$	−238.204	+	412.582i	−0.277951	+	0.481426i	−0.970876	−	0.239585i	$-0.922989\pi$
$857$	−238.204	+	412.582i	−0.277951	+	0.481426i	0.692924	+	0.721011i	$0.256322\pi$
$858$		0			0
$859$	−719.684	+	415.510i	−0.837816	+	0.483714i	−0.856521	−	0.516112i	$-0.827379\pi$
$859$	−719.684	+	415.510i	−0.837816	+	0.483714i	0.0187050	+	0.999825i	$0.494046\pi$
$860$	405.085	+	615.881i	0.471029	+	0.716141i
$861$		0			0
$862$	42.0592	+	140.483i	0.0487926	+	0.162974i
$863$			985.009i			1.14138i	0.821166	+	0.570689i	$0.193324\pi$
$863$			985.009i			1.14138i	−0.821166	+	0.570689i	$0.806676\pi$
$864$		0			0
$865$	−394.607			−0.456193
$866$	1102.23	−	329.996i	1.27279	−	0.381058i
$867$		0			0
$868$	−7.08939	+	4.66293i	−0.00816751	+	0.00537204i
$869$	−470.459	−	814.859i	−0.541380	−	0.937697i
$870$		0			0
$871$	763.655	+	440.897i	0.876757	+	0.506196i
$872$	−264.318	+	315.017i	−0.303117	+	0.361258i
$873$		0			0
$874$	2051.85	+	1935.79i	2.34766	+	2.21487i
$875$	−249.660	−	144.141i	−0.285326	−	0.164733i
$876$		0			0
$877$	−266.136	−	460.961i	−0.303462	−	0.525611i	0.673456	−	0.739227i	$-0.264809\pi$
$877$	−266.136	−	460.961i	−0.303462	−	0.525611i	−0.976918	+	0.213616i	$0.931476\pi$
$878$	−464.436	−	110.070i	−0.528970	−	0.125364i
$879$		0			0
$880$	811.015	+	349.808i	0.921608	+	0.397509i
$881$	−1579.81			−1.79320			−0.896599	−	0.442844i	$-0.853970\pi$
$881$	−1579.81			−1.79320			−0.896599	+	0.442844i	$0.853970\pi$
$882$		0			0
$883$			89.6114i			0.101485i	0.998712	+	0.0507426i	$0.0161588\pi$
$883$			89.6114i			0.101485i	−0.998712	+	0.0507426i	$0.983841\pi$
$884$	−484.697	−	243.414i	−0.548300	−	0.275356i
$885$		0			0
$886$	−101.945	−	24.1605i	−0.115062	−	0.0272692i
$887$	−79.9393	+	46.1530i	−0.0901232	+	0.0520327i	−0.544384	−	0.838836i	$-0.683237\pi$
$887$	−79.9393	+	46.1530i	−0.0901232	+	0.0520327i	0.454261	+	0.890869i	$0.349903\pi$
$888$		0			0
$889$	49.8168	−	86.2853i	0.0560369	−	0.0970588i
$890$	954.958	+	900.943i	1.07299	+	1.01230i
$891$		0			0
$892$	119.302	−	6.95039i	0.133746	−	0.00779192i
$893$	−601.153	+	1041.23i	−0.673184	+	1.16599i
$894$		0			0
$895$	−158.032	+	91.2396i	−0.176572	+	0.101944i
$896$	−15.8768	+	272.850i	−0.0177196	+	0.304520i
$897$		0			0
$898$	−1084.62	+	324.722i	−1.20781	+	0.361606i
$899$		−	18.9163i		−	0.0210415i
$900$		0			0
$901$	−178.922			−0.198582
$902$	−187.372	−	625.848i	−0.207729	−	0.693845i
$903$		0			0
$904$	14.4176	+	2.54186i	0.0159486	+	0.00281179i
$905$	−185.189	−	320.756i	−0.204628	−	0.354427i
$906$		0			0
$907$	−457.854	−	264.342i	−0.504801	−	0.291447i	0.225893	−	0.974152i	$-0.427470\pi$
$907$	−457.854	−	264.342i	−0.504801	−	0.291447i	−0.730694	+	0.682705i	$0.760803\pi$
$908$	−1419.26	+	82.6846i	−1.56306	+	0.0910623i
$909$		0			0
$910$	118.761	−	125.881i	0.130507	−	0.138331i
$911$	291.269	+	168.164i	0.319725	+	0.184593i	0.651270	−	0.758846i	$-0.274237\pi$
$911$	291.269	+	168.164i	0.319725	+	0.184593i	−0.331545	+	0.943439i	$0.607570\pi$
$912$		0			0
$913$	−413.200	−	715.683i	−0.452573	−	0.783880i
$914$	−15.8473	+	66.8672i	−0.0173384	+	0.0731589i
$915$		0			0
$916$	−315.223	−	158.305i	−0.344130	−	0.172822i
$917$	248.027			0.270477
$918$		0			0
$919$		−	1037.58i		−	1.12903i	−0.825423	−	0.564515i	$-0.809063\pi$
$919$		−	1037.58i		−	1.12903i	0.825423	−	0.564515i	$-0.190937\pi$
$920$	−1341.49	+	488.298i	−1.45814	+	0.530759i
$921$		0			0
$922$	125.702	−	530.397i	0.136336	−	0.575268i
$923$	−606.170	+	349.973i	−0.656739	+	0.379169i
$924$		0			0
$925$	−194.667	+	337.172i	−0.210450	+	0.364511i
$926$	776.168	−	822.703i	0.838194	−	0.888448i
$927$		0			0
$928$	−488.737	−	363.821i	−0.526656	−	0.392049i
$929$	−248.930	+	431.159i	−0.267954	+	0.464111i	−0.968333	−	0.249661i	$-0.919681\pi$
$929$	−248.930	+	431.159i	−0.267954	+	0.464111i	0.700379	+	0.713771i	$0.253014\pi$
$930$		0			0
$931$	1330.79	−	768.332i	1.42942	−	0.825276i
$932$	841.228	−	553.303i	0.902605	−	0.593673i
$933$		0			0
$934$	512.775	+	1712.74i	0.549009	+	1.83377i
$935$			808.057i			0.864232i
$936$		0			0
$937$	1236.91			1.32008			0.660039	−	0.751231i	$-0.270540\pi$
$937$	1236.91			1.32008			0.660039	+	0.751231i	$0.270540\pi$
$938$	389.440	−	116.594i	0.415181	−	0.124301i
$939$		0			0
$940$	−334.365	−	508.360i	−0.355707	−	0.540808i
$941$	337.684	+	584.887i	0.358857	+	0.621558i	0.987770	−	0.155917i	$-0.0498333\pi$
$941$	337.684	+	584.887i	0.358857	+	0.621558i	−0.628913	+	0.777476i	$0.716500\pi$
$942$		0			0
$943$	914.466	+	527.967i	0.969741	+	0.559880i
$944$	105.404	+	901.549i	0.111657	+	0.955030i
$945$		0			0
$946$	−773.275	−	729.536i	−0.817415	−	0.771180i
$947$	−160.432	−	92.6256i	−0.169411	−	0.0978095i	0.412897	−	0.910778i	$-0.364517\pi$
$947$	−160.432	−	92.6256i	−0.169411	−	0.0978095i	−0.582308	+	0.812968i	$0.697850\pi$
$948$		0			0
$949$	262.699	+	455.008i	0.276817	+	0.479461i
$950$	−394.405	−	93.4726i	−0.415164	−	0.0983922i
$951$		0			0
$952$	−234.965	+	85.5266i	−0.246812	+	0.0898389i
$953$	399.942			0.419667			0.209833	−	0.977737i	$-0.432708\pi$
$953$	399.942			0.419667			0.209833	+	0.977737i	$0.432708\pi$
$954$		0			0
$955$			770.495i			0.806801i
$956$	−255.397	+	508.557i	−0.267152	+	0.531963i
$957$		0			0
$958$	1051.10	+	249.106i	1.09718	+	0.260027i
$959$	−199.547	+	115.208i	−0.208078	+	0.120134i
$960$		0			0
$961$	−480.006	+	831.396i	−0.499486	+	0.865136i
$962$	−895.147	−	844.515i	−0.930507	−	0.877874i
$963$		0			0
$964$	−13.2682	−	227.745i	−0.0137637	−	0.236250i
$965$	728.071	−	1261.06i	0.754478	−	1.30679i
$966$		0			0
$967$	62.7437	−	36.2251i	0.0648849	−	0.0374613i	−0.467207	−	0.884148i	$-0.654740\pi$
$967$	62.7437	−	36.2251i	0.0648849	−	0.0374613i	0.532091	+	0.846687i	$0.321406\pi$
$968$	−301.123	−	53.0888i	−0.311077	−	0.0548438i
$969$		0			0
$970$	946.205	−	283.283i	0.975469	−	0.292044i
$971$		−	1165.69i		−	1.20051i	−0.799810	−	0.600253i	$-0.795067\pi$
$971$		−	1165.69i		−	1.20051i	0.799810	−	0.600253i	$-0.204933\pi$
$972$		0			0
$973$	320.563			0.329458
$974$	−297.526	−	993.779i	−0.305469	−	1.02031i
$975$		0			0
$976$	704.780	+	946.623i	0.722111	+	0.969900i
$977$	−182.949	−	316.877i	−0.187256	−	0.324337i	0.757078	−	0.653324i	$-0.226626\pi$
$977$	−182.949	−	316.877i	−0.187256	−	0.324337i	−0.944334	+	0.328987i	$0.893293\pi$
$978$		0			0
$979$	−1639.71	−	946.685i	−1.67488	−	0.966992i
$980$	45.2300	+	776.360i	0.0461531	+	0.792205i
$981$		0			0
$982$	206.333	−	218.703i	0.210115	−	0.222712i
$983$	−892.550	−	515.314i	−0.907986	−	0.524226i	−0.0282031	−	0.999602i	$-0.508979\pi$
$983$	−892.550	−	515.314i	−0.907986	−	0.524226i	−0.879782	+	0.475376i	$0.842312\pi$
$984$		0			0
$985$	300.193	+	519.950i	0.304765	+	0.527868i
$986$	128.546	−	542.399i	0.130372	−	0.550100i
$987$		0			0
$988$	574.990	−	1144.94i	0.581974	−	1.15885i
$989$	1718.31			1.73742
$990$		0			0
$991$			1893.70i			1.91090i	0.295148	+	0.955451i	$0.404631\pi$
$991$			1893.70i			1.91090i	−0.295148	+	0.955451i	$0.595369\pi$
$992$	−12.5932	−	29.1913i	−0.0126948	−	0.0294267i
$993$		0			0
$994$	−74.4137	+	313.987i	−0.0748629	+	0.315882i
$995$	−1084.16	+	625.940i	−1.08961	+	0.629085i
$996$		0			0
$997$	644.593	−	1116.47i	0.646533	−	1.11983i	−0.337412	−	0.941357i	$-0.609552\pi$
$997$	644.593	−	1116.47i	0.646533	−	1.11983i	0.983945	−	0.178471i	$-0.0571150\pi$
$998$	−421.158	+	446.408i	−0.422002	+	0.447303i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.f.r.55.1		12
3.2	odd	2		324.3.f.q.55.6		12
4.3	odd	2	inner	324.3.f.r.55.4		12
9.2	odd	6		324.3.d.f.163.1	yes	6
9.4	even	3	inner	324.3.f.r.271.4		12
9.5	odd	6		324.3.f.q.271.3		12
9.7	even	3		324.3.d.e.163.6	yes	6
12.11	even	2		324.3.f.q.55.3		12
36.7	odd	6		324.3.d.e.163.5	✓	6
36.11	even	6		324.3.d.f.163.2	yes	6
36.23	even	6		324.3.f.q.271.6		12
36.31	odd	6	inner	324.3.f.r.271.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.d.e.163.5	✓	6	36.7	odd	6
324.3.d.e.163.6	yes	6	9.7	even	3
324.3.d.f.163.1	yes	6	9.2	odd	6
324.3.d.f.163.2	yes	6	36.11	even	6
324.3.f.q.55.3		12	12.11	even	2
324.3.f.q.55.6		12	3.2	odd	2
324.3.f.q.271.3		12	9.5	odd	6
324.3.f.q.271.6		12	36.23	even	6
324.3.f.r.55.1		12	1.1	even	1	trivial
324.3.f.r.55.4		12	4.3	odd	2	inner
324.3.f.r.271.1		12	36.31	odd	6	inner
324.3.f.r.271.4		12	9.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.91597 + 0.573621i) q^{2} +(3.34192 - 2.19809i) q^{4} +(-2.18740 - 3.78869i) q^{5} +(1.84918 + 1.06762i) q^{7} +(-5.14216 + 6.12848i) q^{8} +O(q^{10})\)	\(q+(-1.91597 + 0.573621i) q^{2} +(3.34192 - 2.19809i) q^{4} +(-2.18740 - 3.78869i) q^{5} +(1.84918 + 1.06762i) q^{7} +(-5.14216 + 6.12848i) q^{8} +(6.36427 + 6.00429i) q^{10} +(-10.9277 - 6.30914i) q^{11} +(-4.63163 - 8.02222i) q^{13} +(-4.15539 - 0.984811i) q^{14} +(6.33682 - 14.6917i) q^{16} +14.6381 q^{17} +34.5778i q^{19} +(-15.6380 - 7.85338i) q^{20} +(24.5563 + 5.81976i) q^{22} +(-35.3255 + 20.3952i) q^{23} +(2.93057 - 5.07589i) q^{25} +(13.4758 + 12.7136i) q^{26} +(8.52653 - 0.496747i) q^{28} +(-9.52010 + 16.4893i) q^{29} +(-0.860391 + 0.496747i) q^{31} +(-3.71373 + 31.7838i) q^{32} +(-28.0462 + 8.39671i) q^{34} -9.34128i q^{35} -66.4263 q^{37} +(-19.8346 - 66.2502i) q^{38} +(34.4668 + 6.07660i) q^{40} +(-12.9434 - 22.4187i) q^{41} +(-36.4816 - 21.0627i) q^{43} +(-50.3877 + 2.93554i) q^{44} +(55.9836 - 59.3401i) q^{46} +(30.1126 + 17.3855i) q^{47} +(-22.2204 - 38.4868i) q^{49} +(-2.70325 + 11.4063i) q^{50} +(-33.1121 - 16.6289i) q^{52} -12.2231 q^{53} +55.2024i q^{55} +(-16.0517 + 5.84275i) q^{56} +(8.78165 - 37.0540i) q^{58} +(-49.1301 + 28.3653i) q^{59} +(-36.8804 + 63.8788i) q^{61} +(1.36354 - 1.44529i) q^{62} +(-11.1164 - 63.0272i) q^{64} +(-20.2625 + 35.0956i) q^{65} +(-82.4391 + 47.5962i) q^{67} +(48.9192 - 32.1758i) q^{68} +(5.35836 + 17.8976i) q^{70} -75.5614i q^{71} -56.7185 q^{73} +(127.271 - 38.1035i) q^{74} +(76.0051 + 115.556i) q^{76} +(-13.4716 - 23.3334i) q^{77} +(64.5777 + 37.2839i) q^{79} +(-69.5232 + 8.12830i) q^{80} +(37.6591 + 35.5290i) q^{82} +(56.7179 + 32.7461i) q^{83} +(-32.0193 - 55.4590i) q^{85} +(81.9798 + 19.4289i) q^{86} +(94.8576 - 34.5279i) q^{88} +150.050 q^{89} -19.7794i q^{91} +(-73.2244 + 145.808i) q^{92} +(-67.6677 - 16.0370i) q^{94} +(131.005 - 75.6355i) q^{95} +(56.4426 - 97.7615i) q^{97} +(64.6505 + 60.9936i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} + 3 q^{4} + 2 q^{5} - 14 q^{8}+O(q^{10}) \) 12 * q + q^2 + 3 * q^4 + 2 * q^5 - 14 * q^8	\( 12 q + q^{2} + 3 q^{4} + 2 q^{5} - 14 q^{8} + 18 q^{10} - 6 q^{13} + 15 q^{16} + 20 q^{17} - 67 q^{20} - 48 q^{22} + 146 q^{26} - 96 q^{28} - 22 q^{29} + 31 q^{32} - 81 q^{34} + 108 q^{37} + 168 q^{38} + 81 q^{40} + 92 q^{41} - 336 q^{44} + 240 q^{46} + 66 q^{49} - 48 q^{50} + 117 q^{52} - 232 q^{53} - 312 q^{56} - 201 q^{58} - 54 q^{61} + 624 q^{62} - 510 q^{64} + 82 q^{65} + 53 q^{68} - 264 q^{70} - 156 q^{73} + 383 q^{74} + 192 q^{76} - 168 q^{77} - 754 q^{80} + 300 q^{82} - 66 q^{85} - 144 q^{86} + 336 q^{88} + 500 q^{89} - 504 q^{92} - 216 q^{94} + 204 q^{97} + 814 q^{98}+O(q^{100}) \) 12 * q + q^2 + 3 * q^4 + 2 * q^5 - 14 * q^8 + 18 * q^10 - 6 * q^13 + 15 * q^16 + 20 * q^17 - 67 * q^20 - 48 * q^22 + 146 * q^26 - 96 * q^28 - 22 * q^29 + 31 * q^32 - 81 * q^34 + 108 * q^37 + 168 * q^38 + 81 * q^40 + 92 * q^41 - 336 * q^44 + 240 * q^46 + 66 * q^49 - 48 * q^50 + 117 * q^52 - 232 * q^53 - 312 * q^56 - 201 * q^58 - 54 * q^61 + 624 * q^62 - 510 * q^64 + 82 * q^65 + 53 * q^68 - 264 * q^70 - 156 * q^73 + 383 * q^74 + 192 * q^76 - 168 * q^77 - 754 * q^80 + 300 * q^82 - 66 * q^85 - 144 * q^86 + 336 * q^88 + 500 * q^89 - 504 * q^92 - 216 * q^94 + 204 * q^97 + 814 * q^98

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